Question

ABC allows employees to purchase two stocks (Stock A and Stock B) to sustain their retirement portfolio. Suppose that there are many stocks in the market, and that the characteristics of Stocks A and B are given as follows:

Stock Expected return Standard deviation

A    10% 5%
B    15% 10%

Note: Correlation = -1

Suppose it is possible to borrow at the risk-free rate, Rf. What must be the value of the risk-free rate?(Hint: think about constructing a risk-free portfolio from Stocks A and B).

Answer 1

There is a perfect negative correlation between A and B. Thus a risk free portfolio can be build and rate of return (in equilibrium) = risk free rate

Let the weight of stock A in portfolio be x and that of B be y. Note that y = 1-x

Portfolio standard deviation = |x*standard deviation of A - y*standard deviation of B|

Thus 0 = |5x - 10*(1-x)|

or x = 0.6667

Now expected rate of return for the portfolio = 0.6667*10% + (1-0.6667)*15%

= 11.67%

Thus the risk free rate = 11.67%